The Cognate Requirement

Rackham requires you to take a non-math course to satisfy the PhD requirements. This is a great opportunity, not to be wasted!  If you have some non-math passion, please consider following it. Students have taken courses on math education policy in the School of Education and courses on Entrepreneurship from Ross, as well as ballet,  Japanese puppet theatre, and Dutch—just about everything.  Alternatively, the cognate requirement is a great opportunity to increase your computing skill. Please help other students by submitting a review for a cognate courses you took at the bottom of this page.

More About the Cognate Requirement

You can take any graduate course you choose (typically any course numbered 400 or above) in another department.  We highly recommend you take something that will increase your skills in computing, statistics, or both, because of the increasing importance of these subjects in mathematics and in society more broadly. But exploring a passion or satisfying a curiosity is also encouraged—not every course you take needs to be directly career related.

Below are some options to consider. Any course on this list of  cross-listed course will satisfy Rackham’s cognate requirement, although we encourage you to look beyond cross-listed courses, too.  AIM students normally choose non-cross-listed courses for cognates. AIM students should talk with the AIM director for more information about program requirements. 

Get  advice from other students and  talk to the particular instructor of these courses for the semester you plan to take it.  Courses can vary dramatically!  Also, shop around a bit, perhaps sitting in a few classes before selecting one.

Suggested Cognate Courses

Stats 525,526 (these are cross-listed with Math, so be sure to sign up for Stats)

Stats 625. A rigorous measure-theory based introduction to probability. It is cross-listed as Math 625, so  register for Stats 625 to get cognate credit.

EECS 402:  Computer Programming for Scientists and Engineers.  This assumes no coding prior experience.

EECS 403:  Graduate Foundations of Data Structures and Algorithms

Stats 415: Introduction to Data Mining.  Students will use the coding language R, but are not assumed to already know it. This is possibly a bit easy for most math students.

Anything numbered over 500   from the School of Information Courses; there are many “lighter” technology courses. One good one in Data Science and Computing is SI 506.

CS 538/PHYS 508:  Network Theory. This course is in the “complex systems” department; it is very mathematical,  though it could depend on the instructor, basically a graph theory course; a small bit of coding is required for some of the units. The other complex systems courses could also be good cognates.

EECS 475/575. Introduction to Cryptography

EECS 477. Introduction to Algorithms. a more mathematical version of the graduate algorithms course EECS 586.

EECS 586. Design and Analysis of Algorithms  Possibly too “easy”: some math students have said that this is very basic math. EECS 477  is apparently a more rigorous algorithms course.

Math 571 (we will sign off on this as an exception, for pure math students only):  Numerical linear algebra underlies much of the data revolution where mathematicians are needed desperately.  Depending on instructor, requires a high-level programming language such as Python or Matlab. Content can vary some with instructors, sometimes more PDEs or more signal processing.

EECS 444/544. Analysis of Societal Networks (may be an ECE course?)

EECS 574. Computational Complexity

EECS 545:  Introduction to Machine Learning. Popular with math students; students with strong linear algebra (most math grads) can go straight to this instead of  EECS 445, as long as they are comfortable with whatever coding language is being used (varies with instructor). EECS 445 will review more linear algebra concepts first.

EECS 551. Matrix Methods for Signal Processing, Data Analysis and
Machine Learning. Similar to Math 571 but more  more applied.


Several units on campus offer “Certifications”  which are like  mini-masters degrees. Students should consider these to broaden their interests and education, as well as to  increase the attractiveness resume for both academic and non-academic positions.

Rackham maintains a Complete list of Rackham Certifications  in a broad array of fields, including various Professional Development certification in things such as Diversity, Equity and Inclusion. In particular, many are in technical fields that are relatively easy and can be quite helpful for math students.  Certification in a technical field typically requires taking about 3 courses from a long list,  many of which are in math.  The courses listed as options for a particular certification can give good ideas for students looking for a cognate in particular directions.

The following certifications are especially recommended for Math and AIM students:

  1. Data Science Certificate from MIDAS: brief description. Talk to Professor Anna Gilbert.
  2. Graduate Certificate in Scientific Computing offered by MICDE:   brief description talk to Professors Silas Alben or Victoria Booth
  3. Complex Systems from  CSCS:  brief description. Talk to Professors Charlie Doering or Victoria Booth. 

Suggest a Cognate

Please help other students by writing reviews of cognate courses! Just fill in the form and we will add your advice.